5/(1+x) = 3 – 4/(x-1)
5/(1+x) = 3(x-1)/x-1 – 4/(x-1)
5/(1+x) = (3x– 7)/(x-1)
5(x-1)/(1+x)(x-1) = (3x– 7)(1+x)/(x-1)(1+x)
(5x-5)/(x-1+x^2-x) = (3x+3x^2-7-7x)/(x-1+x^2-x)
5x-5 = 3x^2 - 7 - 4x
(3x^2 - 9x – 12)/3 = 0
x^2 – 3x – 4 = 0
x = - (3/2) ± √ (3/2)^2 + 4
x = -1,5 ± √ 6,25
x = -1,5 ± 2.5
x1 = 1
x2 = -4
Answer is suppost to be
x1 = -0,21
x2 = 3,21
Where did I go wrong? :D
Solve for x:
5/(x + 1) = 3 - 4/(x - 1)
Bring 3 - 4/(x - 1) together using the common denominator x - 1:
5/(x + 1) = (3 x - 7)/(x - 1)
Cross multiply:
5 (x - 1) = (x + 1) (3 x - 7)
Expand out terms of the left hand side:
5 x - 5 = (x + 1) (3 x - 7)
Expand out terms of the right hand side:
5 x - 5 = 3 x^2 - 4 x - 7
Subtract 3 x^2 - 4 x - 7 from both sides:
-3 x^2 + 9 x + 2 = 0
Divide both sides by -3:
x^2 - 3 x - 2/3 = 0
Add 2/3 to both sides:
x^2 - 3 x = 2/3
Add 9/4 to both sides:
x^2 - 3 x + 9/4 = 35/12
Write the left hand side as a square:
(x - 3/2)^2 = 35/12
Take the square root of both sides:
x - 3/2 = sqrt(35/3)/2 or x - 3/2 = -sqrt(35/3)/2
Add 3/2 to both sides:
x = 3/2 + sqrt(35/3)/2 or x - 3/2 = -sqrt(35/3)/2
Add 3/2 to both sides:
Answer: | x = 3/2 + sqrt(35/3)/2 or x = 3/2 - sqrt(35/3)/2
5/(1+x) = 3 – 4/(x-1)
Answer is suppost to be
x1 = -0,21
x2 = 3,21
Where did I go wrong? :D
\(\frac{5}{1+x}=3-\frac{4}{x-1}\)
\(\frac{5}{1+x}+\frac{4}{x-1}=3\)
\(\frac{5x-5+4+4x}{x^2-1}=3\)
\({9x-1}=3x^2-3\)
\(3x^2-9x-2=0\)
\(x^2-3x-\frac{2}{3}=0\)
\(x_1=1.5+\sqrt{2.25+\frac{2}{3}}\)
\(x=1.5\pm\sqrt{2.91\overline{66}}\)
\(x_1=3.2078\\x_2=-0.2078\)
!